Public key digital signatures are important for secure exchange of information between plural parties, for example between computers or mobile devices, or between a smart card and a terminal.
A digital signature and authentication method and apparatus, which has in the past demonstrated advantageous operation, is described in U.S. Pat. No. 7,308,097, assigned to the same assignee as the present Application, incorporated by reference, and sometimes referred to as “NTRUSign” (mark of NTRU Cryptosystems, Inc.). Reference can also be made to “NTRUSign: Digital Signatures Using the NTRU Lattice”, J. Hoffstein, N. Howgrave Graham, J. Pipher, J. Silverman, and W. Whyte, Topics In Cryptology-CT-RSA 2003, Lecture Notes in Computer Science, Vol. 2612, Springer, Berlin, 2003, also incorporated by reference.
The signing technique in the '097 Patent uses a mixing system based on multiplication in a ring and reduction modulo an ideal q in that ring; while the verification technique uses special properties of products of elements whose validity depends on elementary probability theory. The security of the identification/digital signature scheme comes from the interaction of reduction modulo q and the difficulty of forming products with special properties. In an embodiment of the digital signature scheme of the '097 Patent, the security also relies on the experimentally observed fact that for most lattices, it is very difficult to find a vector whose length is only a little bit longer than the shortest vector, and it is also difficult to find a lattice vector that is quite close to a randomly chosen nonlattice vector.
Although the technique of the '092 Patent has provided acceptable performance, and has exhibited good security, there is a need for an improved digital signature technique that is more efficient to use and has even better security. It is among the objectives of the present invention to provide improvement over the technique of the '092 Patent and over other prior art techniques relating to digital signatures.